Polygons Help!

Okay, I've posted after a long time, I know... But I'm here with another doubt.
The ratio between the sides of 2 regular polygons is 4 : 5 and the ratio between the interior angles is 15 : 16. Find the number of sides.

Okay, I've posted after a long time, I know... But I'm here with another doubt.
The ratio between the sides of 2 regular polygons is 4 : 5 and the ratio between the interior angles is 15 : 16. Find the number of sides.

Thanks!

Let the number of sides of the polygons be and , then the first condition tell you that:

,

and as the interior angle of a ploygon with sides is , the second condition tells us that:

which may be simplified as we know to:

Now we can proceed to solve and , or we can just guess, when we find , .